Pseudo One-compartment Model Research Articles

Phosphate Kinetics in Hemodialysis: Application of Delayed Pseudo One-Compartment Model

Background/Aims: Various body-regulating mechanisms try to counteract rapid changes in serum phosphate levels during hemodialysis (HD). Neither recently proposed nor other existing standard compartment models are able to capture clinically observed intradialytic serum phosphate rebound. Methods: Phosphate serum concentration was frequently measured during 75 HD sessions in 25 patients. Time delay was introduced into the standard pseudo one-compartment model in order to reflect the time needed for the body-regulating mechanism to affect serum phosphate level. Results: Measured serum phosphate concentration at the end of 4 h dialysis session was on average larger than 1 h earlier (p value = 0.015). The model with time delay reproduced successfully 19 out of 21 and 9 out of 10 sessions with and without recorded intradialytic rebound, respectively. Conclusion: The intradialytic serum phosphate rebound is associated with the time delay reflecting efficacy of body-regulating mechanisms, that is, the larger the delay the larger is the intradialytic rebound.

Prescriptions of dialysate potassium concentration during short daily or long nocturnal (high dose) hemodialysis.

The prescription of dialysate potassium concentration during short daily and long nocturnal (high dose) hemodialysis (HD) is challenging due to limited clinical experience with such modalities. The aim here is to propose a quantitative approach for prescribing dialysate potassium concentrations during high-dose HD. Potassium kinetic parameters based on a pseudo one-compartment model from 547 patients participating in the HEMO Study were used for prediction purposes in this study. Patients were categorized based on the prescribed dialysate potassium concentration during thrice weekly HD as 1K (mean of 1.02 mEq/L, N = 60), 2K (2.01 mEq/L, N = 437), or 3K (3.01 mEq/L, N = 50). Dialysate potassium concentrations were then predicted for each patient during short daily and long nocturnal HD based on a pseudo one-compartment model to maintain the identical weekly dialytic potassium removal and predialysis serum potassium concentration as during thrice weekly HD. Predicted prescribed dialysate potassium concentrations for short daily HD were 0.18-0.45 mEq/L higher than during thrice weekly HD but were approximately 4 (3.72-4.26) mEq/L for all patients during long nocturnal HD. The intradialytic decrease in serum potassium concentration was predicted to be reduced by more than one-half during short daily HD and by approximately three-quarters during long nocturnal HD of that during thrice weekly HD. Prescribed dialysate potassium concentration during high-dose HD modalities can be quantitatively predicted using a pseudo one-compartment kinetic model. High-dose HD modalities may improve clinical outcomes by reducing intradialytic decreases in serum potassium.

Phosphate Kinetics During Weekly Cycle of Hemodialysis Sessions: Application of Mathematical Modeling.

Both hyperphosphatemia and hypophosphatemia are associated with increased morbidity and mortality among patients on dialysis. The control of serum phosphate concentration is a considerable clinical problem. Our study aimed to improve understanding of phosphate kinetics in patients on dialysis using mathematical modeling. Three consecutive hemodialysis sessions with breaks of 2-2-3 days were monitored in 25 patients. Phosphate concentration was measured every hour and 45 min after the end of dialysis in blood serum and every 30 min in dialysate during each session. Volume of fluid compartments and body composition were assessed by bioimpedance. The pseudo one-compartment model was applied to describe the profile of phosphate in blood serum during intra- and interdialytic periods of 1-week cycle of three hemodialysis sessions. Model parameters, such as phosphate internal clearance (KM ) and the rate of phosphate mobilization (RM ), were correlated with the reduction of serum phosphate concentration during dialysis (Cpost /Cpre ) and with equivalent continuous clearance (ECC) for phosphate. KM correlated negatively with predialysis serum phosphate concentration. There was significant positive correlation between RM and age. Postdialysis volume of phosphate central compartment was lower than, but correlated to, extracellular water volume. Parameters of the pseudo one-compartment model, phosphate internal clearance, and the rate of phosphate inflow to the central compartment (the one accessible for dialysis) from other phosphate body reservoirs correlated with the indices of dialysis adequacy, such as reduction of serum phosphate and ECC. The pseudo one-compartment model can be successfully extended from a single hemodialysis to the standard weekly cycle of sessions and the model parameters strongly correlate with the adequacy parameters of dialytic removal of phosphate.

Potassium kinetics during hemodialysis.

Hyperkalemia in hemodialysis patients is associated with high mortality, but prescription of low dialysate potassium concentrations to decrease serum potassium levels is associated with a high incidence of sudden cardiac arrest or sudden death. Improved clinical outcomes for these patients may be possible if rapid and substantial intradialysis decreases in serum potassium concentration can be avoided while maintaining adequate potassium removal. Data from kinetic modeling sessions during the HEMO Study of the dependence of serum potassium concentration on time during hemodialysis treatments and 30 minutes postdialysis were evaluated using a pseudo one-compartment model. Kinetic estimates of potassium mobilization clearance (K(M)) and predialysis central distribution volume (V(pre)) were determined in 551 hemodialysis patients. The studied patients were 58.8 ± 14.4 years of age with predialysis body weight of 72.1 ± 15.1 kg; 306 (55.4%) of the patients were female and 337 (61.2%) were black. K(M) and V(pre) for all patients were non-normally distributed with values of 158 (111, 235) (median [interquartile range]) mL/min and 15.6 (11.4, 22.8) L, respectively. K(M) was independent of dialysate potassium concentration (P > 0.2), but V(pre) was lower at higher dialysate potassium concentration (R = -0.188, P < 0.001). For patients with dialysate potassium concentration between 1.6 and 2.5 mEq/L (N = 437), multiple linear regression of K(M) and V(pre) demonstrated positive association with predialysis body weight and negative association with predialysis serum potassium concentration. Potassium kinetics during hemodialysis can be described using a pseudo one-compartment model.

Simplified phosphorus kinetic modeling: predicting changes in predialysis serum phosphorus concentration after altering the hemodialysis prescription

The KDIGO work group recommends increasing dialytic phosphorus removal in Stage 5D chronic kidney disease patients with persistent hyperphosphatemia; however, optimal prescriptions to enhance phosphorus removal by hemodialysis (HD) therapies have not yet been established. This study evaluated whether phosphorus kinetic modeling based on a pseudo one-compartment model could provide practical clinical guidance for predicting changes in predialysis serum phosphorus concentration after altering the HD prescription. Patient-specific phosphorus kinetic parameters determined from thrice weekly HD treatments on 774 patients in the HEMO Study were used to predict changes in predialysis serum phosphorus concentration after altering the HD prescription from thrice weekly to short daily and long nocturnal HD therapies. The effect of changes in the oral phosphorus binder prescription on predicted changes in the predialysis serum phosphorus concentration was also illustrated using the concept of equivalent phosphorus binder dose. Decreases in predialysis serum phosphorus concentration from thrice weekly HD to short daily and long nocturnal HD prescriptions demonstrated strong associations with the predialysis serum phosphorus concentration during thrice weekly HD that were relatively independent of patient-specific phosphorus kinetic parameters. Thus, the percent decrease in predialysis serum phosphorus concentration was approximately the same among patients for a given alteration in the HD prescription. Both increased weekly treatment time and frequency resulted in a reduction in the predialysis serum phosphorus concentration; however, the effect of treatment time was more influential. Simultaneous reduction in the effective phosphorus binder dose blunted the decrease in the predialysis serum phosphorus concentration. This study demonstrated that a simplified form of phosphorus kinetic modeling based on a pseudo one-compartment model can provide practical clinical guidance for predicting changes in predialysis serum phosphorus concentration after altering the HD prescription. Prospective validation of this approach in future studies is warranted.

Determinants of phosphorus mobilization during hemodialysis

Our recent work proposed a pseudo one-compartment model for describing intradialysis and postdialysis rebound kinetics of phosphorus. In this model, phosphorus is removed directly from a central distribution volume with the rate of phosphorus mobilization from a second, very large compartment proportional to the phosphorus mobilization clearance. Here, we evaluated factors of phosphorus mobilization clearance and postdialysis central distribution volume from 774 patients in the HEMO Study. Phosphorus mobilization clearance and postdialysis central distribution volume were 87 (65, 116) ml/min, median (interquartile range), and 9.4 (7.2, 12.0) liter, respectively. The phosphorus mobilization clearance was significantly higher for male patients than for female patients. Both the phosphorus mobilization clearance and the postdialysis central distribution volume were significantly associated with postdialysis body weight but negatively with the predialysis serum phosphorus concentration. The postdialysis central distribution volume was also significantly associated with age. Overall, the postdialysis central distribution volume was 13.6% of the postdialysis body weight. Thus, the phosphorus mobilization clearance during hemodialysis is higher when predialysis serum phosphorus concentration is low and higher in male patients than in female patients. The central distribution volume of phosphorus is a space approximating the extracellular fluid volume.

Physiologic volume of phosphorus during hemodialysis: Predictions from a pseudo one‐compartment model

The kinetics of plasma phosphorus concentrations during hemodialysis (HD) are complex and cannot be described by conventional one- or two-compartment kinetic models. It has recently been shown by others that the physiologic (or apparent distribution) volume for phosphorus (Vr-P) increases with increasing treatment time and shows a large variation among patients treated by thrice weekly and daily HD. Here, we describe the dependence of Vr-P on treatment time and predialysis plasma phosphorus concentration as predicted by a novel pseudo one-compartment model. The kinetics of plasma phosphorus during conventional and six times per week daily HD were simulated as a function of treatment time per session for various dialyzer phosphate clearances and patient-specific phosphorus mobilization clearances (K(M)). Vr-P normalized to extracellular volume from these simulations were reported and compared with previously published empirical findings. Simulated results were relatively independent of dialyzer phosphate clearance and treatment frequency. In contrast, Vr-P was strongly dependent on treatment time per session; the increase in Vr-P with treatment time was larger for higher values of K(M). Vr-P was inversely dependent on predialysis plasma phosphorus concentration. There was significant variation among predicted Vr-P values, depending largely on the value of K(M). We conclude that a pseudo one-compartment model can describe the empirical dependence of the physiologic volume of phosphorus on treatment time and predialysis plasma phosphorus concentration. Further, the variation in physiologic volume of phosphorus among HD patients is largely due to differences in patient-specific phosphorus mobilization clearance.

Patient-specific phosphorus mobilization clearance during nocturnal and short daily hemodialysis

The kinetics of plasma phosphorus during different hemodialysis (HD) modalities are incompletely understood. We recently demonstrated that a pseudo one-compartment kinetic model including phosphorus mobilization from various body compartments into extracellular fluids can describe intradialytic and postdialytic rebound kinetics of plasma phosphorus during conventional and short 2-hour HD treatments. In this model, individual patient differences in phosphorus kinetics were characterized by a single parameter, the phosphorus mobilization clearance (K(M)). In this report we determined K(M) in patients treated by in-center nocturnal HD (ICNHD) and short daily HD (SDHD) with low dialyzer phosphate clearance. In the ICNHD study, eight patients underwent 8-hour HD treatments where intradialytic and postdialytic plasma samples were collected; K(M) values were determined by nonlinear regression of plasma concentration as a function of time. In the SDHD study, five patients were studied during 28 treatments for approximately 3 hours. Here, K(M) was calculated using only predialytic and postdialytic plasma phosphorus concentrations. Dialyzer phosphate clearances were 134 ± 20 (mean ± SD) and 95 ± 16 mL/min during ICNHD and SDHD, respectively. K(M) values for the respective therapies were 124 ± 83 and 103 ± 33 mL/min, comparable to those determined previously during conventional and short HD treatments of 98 ± 44 mL/min. When results from ICNHD, SDHD, and previous HD modalities were combined, K(M) was directly correlated with postdialytic body weight (r = 0.38, P = 0.025) and inversely correlated with predialytic phosphorus concentration (r = -0.47, P = 0.005). These findings suggest that phosphorus kinetics during various HD modalities can be described by a pseudo one-compartment model.

Kinetic Model of Phosphorus Mobilization during and after Short and Conventional Hemodialysis

The kinetics of plasma phosphorus (inorganic phosphorus or phosphate) during hemodialysis treatments cannot be explained by conventional one- or two-compartment models; previous approaches have been limited by assuming that the distribution of phosphorus is confined to classical intracellular and extracellular fluid compartments. In this study a novel pseudo one-compartment model, including phosphorus mobilization from a large second compartment, was proposed and evaluated. Clinical data were obtained during a crossover study where 22 chronic hemodialysis patients underwent both short (2-hour) and conventional (4-hour) hemodialysis sessions. The model estimated two patient-specific parameters, phosphorus mobilization clearance and phosphorus central distribution volume, by fitting frequent intradialytic and postdialytic plasma phosphorus concentrations using nonlinear regression. Phosphorus mobilization clearances varied among patients (45 to 208 ml/min), but estimates during short (98 ± 44 ml/min, mean ± SD) and conventional (99 ± 47 ml/min) sessions were not different (P = 0.74) and correlated with each other (concordance correlation coefficient ρ(c) of 0.85). Phosphorus central distribution volumes for each patient (short: 11.0 ± 4.2 L and conventional: 11.9 ± 3.8 L) were also correlated (ρ(c) of 0.45). The reproducibility of patient-specific parameters during short and conventional hemodialysis treatments suggests that a pseudo one-compartment model is robust and can describe plasma phosphorus kinetics under conditions of clinical interest.

A simple method to estimate phosphorus mobilization in hemodialysis using only predialytic and postdialytic blood samples

We have recently developed a pseudo one-compartment model to describe intradialytic and postdialytic rebound kinetics of plasma phosphorus. In this model, individual patient differences in phosphorus kinetics were characterized by a single parameter; the phosphorus mobilization clearance (K(M) ). In this work, we propose a simple method to estimate K(M) from predialytic and postdialytic plasma phosphorus concentrations. Clinical data were collected from 22 chronic hemodialysis patients that underwent a 4-hour treatment session. A simple algebraic equation was derived from the pseudo one-compartment model to determine K(M) from predialytic and postdialytic plasma phosphorus concentrations. K(M) values computed using this equation were compared with values obtained from nonlinear regression of the full kinetic model to frequent intradialytic and postdialytic measurements of plasma phosphorus concentrations. There was good agreement between K(M) values (concordance correlation coefficient of 0.94) obtained from the simple method (105 ± 52 mL/min, mean ± SD) and from the full model (99 ± 47 mL/min). The 95% confidence interval for the difference between estimated K(M) values was -26 to 36 mL/min. The proposed simple method requires the use of only predialytic and postdialytic blood samples to estimate patient specific K(M) ; this approach may allow easy clinical evaluation of phosphorus kinetics in hemodialysis patients.